The survey of Tory constituency chairmen, seen by The Sunday Telegraph, finds that 71 per cent think the proposal - which the Prime Minister has pledged will be law by 2015 - should be abandoned.

Nearly half the chairmen claim their local parties have lost members as a result of the plans, while only three per cent say they have gained membership.

Ministers have vowed to press on after a consultation on proposals to legalise gay marriage in England and Wales and to enable existing civil partners to “convert” into a civil marriage.

Mr Cameron, Ed Miliband and Nick Clegg all support the plans - with the Deputy Prime Minister becoming embroiled in a row last month after a draft version of a speech described opponents of gay marriage as "bigots".

Religious organisations would not be compelled to conduct same-sex marriages in their places of worship. However, the Church of England and other religious bodies have criticised the impact of the plans on the institution of marriage as a whole.

Today’s ComRes poll for the Coalition for Marriage, the campaign group which opposes any change to the law, shows that such concerns are also prevalent throughout local Tory associations as party activists gather for their annual conference in Birmingham this week.

In a message aimed at the Prime Minister personally, only one in 10 local chairmen says the plans have enhanced Mr Cameron’s standing with the party, while 70 per cent say they have made it worse.

Just 11 per cent say same-sex marriage should be a political priority right now, at a time when Whitehall spending is facing deep cut and ministers are driving forward key reforms in education, health and welfare. Almost three quarters of those questioned (73 per cent) say it should not.

Overall, 71 per cent of chairmen believe most Tory members in their constituencies oppose the government’s same-sex marriage proposals - including 47 per cent who believe members “strongly” object to the plans.

Mr Cameron said in August he was “absolutely determined” that the coalition would legislate for gay marriage “in this Parliament.” This followed suggestions in May that he would allow MPs a free vote on gay marriage — making its progress into law by 2015 much harder, as many Tory MPs do not support the move.

The Prime Minister compared his opponents in the Church to his own party “which for many many years got itself on the wrong side of this argument”.

He added in August: “It locked people out who were naturally Conservative from supporting it and so I think I can make that point to the Church, gently.” In last month’s reshuffle, ministerial responsibility for the policy shifted from Lynne Featherstone, a Liberal Democrat, to Maria Miller, the new Tory culture secretary - again sparking claims that the government was giving ground to opponents.

However, Ms Miller said its introduction would be a milestone in Britain’s heritage “of freedom and fairness”.

She added: “The state should not stop two people undertaking civil marriage unless there are good reasons, and I believe being gay is not one of them.”

*ComRes surveyed 100 Conservative party constituency chairmen between 14 September and 2 October.